Do you want to publish a course? Click here

Poincare inequalities on intervals -- application to sensitivity analysis

117   0   0.0 ( 0 )
 Added by Olivier Roustant
 Publication date 2016
  fields
and research's language is English




Ask ChatGPT about the research

The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincare inequalities. Typically two kind of sensitivity indices are linked by a Poincare type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper to compute. This allows performing a low-cost screening of unessential variables. The efficiency of this screening then highly depends on the accuracy of the upper bounds in Poincare inequalities. The novelty in the questions concern the wide range of probability distributions involved, which are often truncated on intervals. After providing an overview of the existing knowledge and techniques, we add some theory about Poincare constants on intervals, with improvements for symmetric intervals. Then we exploit the spectral interpretation for computing exact value of Poincare constants of any admissible distribution on a given interval. We give semi-analytical results for some frequent distributions (truncated exponential, triangular, truncated normal), and present a numerical method in the general case. Finally, an application is made to a hydrological problem, showing the benefits of the new results in Poincare inequalities to sensitivity analysis.



rate research

Read More

Global sensitivity analysis (GSA) of numerical simulators aims at studying the global impact of the input uncertainties on the output. To perform the GSA, statistical tools based on inputs/output dependence measures are commonly used. We focus here on dependence measures based on reproducing kernel Hilbert spaces: the Hilbert-Schmidt Independence Criterion denoted HSIC. Sometimes, the probability distributions modeling the uncertainty of inputs may be themselves uncertain and it is important to quantify the global impact of this uncertainty on GSA results. We call it here the second-level global sensitivity analysis (GSA2). However, GSA2, when performed with a double Monte Carlo loop, requires a large number of model evaluations which is intractable with CPU time expensive simulators. To cope with this limitation, we propose a new statistical methodology based on a single Monte Carlo loop with a limited calculation budget. Firstly, we build a unique sample of inputs from a well chosen probability distribution and the associated code outputs are computed. From this inputs/output sample, we perform GSA for various assumed probability distributions of inputs by using weighted HSIC measures estimators. Statistical properties of these weighted esti-mators are demonstrated. Finally, we define 2 nd-level HSIC-based measures between the probability distributions of inputs and GSA results, which constitute GSA2 indices. The efficiency of our GSA2 methodology is illustrated on an analytical example, thereby comparing several technical options. Finally, an application to a test case simulating a severe accidental scenario on nuclear reactor is provided.
To estimate direct and indirect effects of an exposure on an outcome from observed data strong assumptions about unconfoundedness are required. Since these assumptions cannot be tested using the observed data, a mediation analysis should always be accompanied by a sensitivity analysis of the resulting estimates. In this article we propose a sensitivity analysis method for parametric estimation of direct and indirect effects when the exposure, mediator and outcome are all binary. The sensitivity parameters consist of the correlation between the error terms of the mediator and outcome models, the correlation between the error terms of the mediator model and the model for the exposure assignment mechanism, and the correlation between the error terms of the exposure assignment and outcome models. These correlations are incorporated into the estimation of the model parameters and identification sets are then obtained for the direct and indirect effects for a range of plausible correlation values. We take the sampling variability into account through the construction of uncertainty intervals. The proposed method is able to assess sensitivity to both mediator-outcome confounding and confounding involving the exposure. To illustrate the method we apply it to a mediation study based on data from the Swedish Stroke Register (Riksstroke).
In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Lo`eve expansions. We construct efficient estimators for the drift of such processes, and prove their minimaxity using Bayes estimators. We also construct superefficient estimators of Stein type for such drifts using the Malliavin integration by parts formula and stochastic analysis on Gaussian space, in which superharmonic functionals of the process paths play a particular role. Our results are illustrated by numerical simulations and extend the construction of James-Stein type estimators for Gaussian processes by Berger and Wolper.
228 - Xinjia Chen 2014
We explore the applications of our previously established likelihood-ratio method for deriving concentration inequalities for a wide variety of univariate and multivariate distributions. New concentration inequalities for various distributions are developed without the idea of minimizing moment generating functions.
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our development complements recent results by Wei and Dudley (2011) concerning exponential bounds for two-sided Kolmogorov - Smirnov statistics by giving corresponding results for one-sided statistics with emphasis on adjusted inequalities of the type proved originally by Dvoretzky, Kiefer, and Wolfowitz (1956) and by Massart (1990) for one-samp
comments
Fetching comments Fetching comments
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا